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A relaxed constant positive linear dependence constraint qualification and applications |
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| Authors: | Roberto Andreani Gabriel Haeser María Laura Schuverdt Paulo J S Silva |
| Institution: | 1. Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Campinas, SP, Brazil 2. Institute of Science and Technology, Federal University of S?o Paulo, S?o José dos Campos, SP, Brazil 3. CONICET, Department of Mathematics, FCE, University of La Plata, CP 172, 1900, La Plata, Bs. As., Argentina 4. Institute of Mathematics and Statistics, University of S?o Paulo, S?o Paulo, SP, Brazil |
| Abstract: | In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie’s constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ. |
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